Jimmy Howard had to make just 19 saves to collect his sixth shutout of the season.
Detroit won its second in a row after losing three straight and moved two points in front of St. Louis for the lead in the Central Division. The Red Wings have 89 points, tied with the New York Rangers one point behind Vancouver for the most in the NHL.
Filppula beat Josh Harding with a backhand shot to open the scoring and his slap shot with 3:25 to go in the second period gave the Red Wings a 4-0 lead.
Brendan Smith, Darren Helm, Ian White and Henrik Zetterberg also scored.
Harding gave up all six goals on 29 shots before being replaced in the third period by Matt Hackett.
Howard has 10 shutouts in his three full seasons as Detroit's goaltender. His six this season are twice as many as he has had in any other season.